dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day! A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

A critical point is a point of a function where the gradient is zero or not defined (the derivative is equal to 0 or the derivative is not real). A critical point is similar to a stationary point (except for the undefined part) its value maybe maximum / minimum local / global.

How to calculate critical points?

From the function $ f $, calculate its derivative $ f '$ and look at the critical values for which it cancels $ f'(x) = $ 0 or the values for which it is not defined (see domain derivability).

Example: The square root function $ f(x) = \sqrt{x} $ has for derivative $ f'(x) = \frac{1}{2\sqrt{x}} $ which is not defined (over the reals) for $ x <= 0 $, its critical values are therefore all negative numbers (including 0).

What is the difference between a critical point and a stationary point?

A critical point is the union of all the points where the derivative is zero (called stationary points) with all the points or the derivative is not defined (called singular points).

dCode retains ownership of the online "Critical Point of a Function" source code. Except explicit open source licence (indicated CC / Creative Commons / free), the "Critical Point of a Function" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Critical Point of a Function" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, copy-paste, or API access for "Critical Point of a Function" are not public, same for offline use on PC, tablet, iPhone or Android ! Remainder : dCode is free to use.

Need Help ?

Please, check our dCode Discord community for help requests! NB: for encrypted messages, test our automatic cipher identifier!

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developed the best 'Critical Point of a Function' tool, so feel free to write! Thank you!

Thanks to your feedback and relevant comments, dCode has developed the best 'Critical Point of a Function' tool, so feel free to write! Thank you!